For the purpose of reducing their carbon footprint, many heat exchangers for bathing showers used in households have been introduced in the market. The design concept is that incoming cold tap water running through the heat exchanger is heated up by hot waste water from the shower, which serves as a thermal source, so that the temperature of the tap water output from the heat exchanger becomes warmer than that of the incoming tap water, the output being directed into an inlet pipe for the water heater of the bathing shower. As a result, the temperature of the inlet water for the water heater of the bathing shower is increased to save energy required for heating the water. However, due to the complicated structural design of these currently marketed heat exchangers, the manufacturing process and related machinery are relatively complex, so that not only are the selling price and manufacturing cost kept at a high level without possibility of lowering, but marketing promotion and popularity are retarded, discouraging purchasing and use by consumers and thereby limiting benefits to the environment. Therefore, simplification of the structural design and reduction in manufacturing costs of heat exchangers for bathing showers has become a critical need.